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24 Cards in this Set

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THE 5 KEY WORDS OF COMPETENACY 13
PATTERNS
SEQUUENCES
ALGEBRIAC MANIPULAITON
FUNCTION
MULTIPLE REPRESENTAION
S
A
F
M
FIRST OF COMP 13 DESCRIPTOR HIGHLIHTSOF THIS COMPETENC
THE ESSENCE OF THIS COMPETENCY IS TO BE ABLE TO MOVE FROM ONE MODE OF REPRESENTATION FOR SEQUENCES AND FUNCTIONS
TO MOVE TO A NEW MODE
SECOND OF COMP 13 DESCRIPTOR HIGHLIHTSOF THIS COMPETENCY
FOR VARIABLES, EXPRESSIONS, EQUATIONS, INEQUALITIES RELATIONS AND FUNCTIONS=THE FOCUS IS ON THE RELTIONSHIPS AMONG THEM
THE FOCUS IS ON THE RELAITONSHIPS
COMP 13-PATTERNS USING MULTIPLE REPRESENTATIONS-GIVE AN EXAMPLE OF A CONCRETE VISUAL MODEL
SOMETHING LIKE A TRIANGLE WITH THREE LITTLE TRIANGLES POINTED TO EACH OTHER ON THE INSIDE-PREDICT THE NUMBER OF
PREDICT THE NUMBER OF TRIANGLES IN THE NEXT TWO LAYERS-
eXTEND THE SIDES OF THE TRIANGLE AND THE LINES PARALLEL TO THEM TO DRAW THE NEXT TWO LAYERS
PREDICT THE NUMBER OF TRIANGLES AND THE PARALLEL TO THEM TO DRAW THE NEXT TWO LAYERS
PATTERNS INVOLVING REPRESENTAION-TABLE
NUMBOFTRMS|PROC.COLUMN|TERM
1 | 1 PLUS 0 }1
2 } 2+1 }3
3 } 3+2 } 5
4 | 4+3 | 7
5 | 5+4 | 9
N | N+N-1
DO YOU UNDERSTAND THE LAST PART OF THE TABLE
THE BASIC GRAPH
RISE/RUN
VERBAL DESCRIPTION
value of the ter=two times the term number minus one
ALGEBRAIC EXPRESSIONS
MAKE A PROCESS COLUMN
WRITE AN ALGEBRA FORMULA USING N AS THE TERM NUMBER TO PREDICT THE VALUE OF ANY TERM IN A SEQUENCE: iF YOU BUILD A PROCESS COULUMN, YOU CAN DETERIMINE THE FORMULA MORE EASILY f(n)=2n-1
iF YOU BUILD A PROCESS COULUMN, YOU CAN DETERIMINE THE FORMULA MORE EASILY f(n)=2n-1
YOU CAN USE SEQUENCES OF MULTIPLE REPRESENTATIONS HOW
THE SEQUENCE CAN BE GEERATED FROM ANY OF THE REPRESENTATIONS YOU CAN START AT ANY ONE OF THE REPRESENTATIONS AND MOVE TO THE NEXT ONE.
FUCTIONS USING MULTIPLE REPRESENTATIONS-DEFINE A FUNCTION
A SET OF POINTS (X,Y) WITH EXACTLY ONE DISCTINCT VALUE OF Y FOR EVERY VALUE OF X
DEFINE A FUNCTION
FUCTIONS USING MULTIPLE REPRESENTATIONS-NAME THE 5 MODES OF REPRESENT
VERBAL
PICTORIAL
TABULAR
GRAPHICAL
SYMBOLIC
V
P
T
G
S
FUCTIONS USING MULTIPLE REPRESENTATIONS-VERBAL EXAMPLE
A COUPLE IS PLAINNING TO PUT A RUG IN ONE CORNER OF THEIR FAMILY ROOM, LEAVING A STRIP OF FLOOR THE SAME WIDTH ON TWO SIDES OF THE ROOM. THE DIMENSIONS OF THE ROOM ARE 4 METES BY 6 METERS, WRITE AN EXPRESSION TO REPRESENT THIS FUCTION
VERBAL
FUCTIONS USING MULTIPLE REPRESENTATIONS-PICTORIAL
A SQUARE SHAPE WITH 6 METERS ON TOP>>>>>>>>>>>>
4 METERS AS THE WIDTHE
PICTORIAL
FUCTIONS USING MULTIPLE REPRESENTATIONS-TABULAR
W OF |LENGTH|WIDTH| AREA
UNCARPET |
STRIP LOOK AT PAGE 56
OF FLOOR
0 6 4 24
1 5 3 15
TABULAR
FUCTIONS USING MULTIPLE REPRESENTATIONS-GRAPHIC
THE AREA (0 TO 24)WOULD BE ON THE Y AXIS A(0,10) AND THE WIDTH OF UNCARPETED PEOPLE
GRAPHIC
FUCTIONS USING MULTIPLE REPRESENTATIONS-SYMBOLIC
X=WIDTH OF UNCARPTETED FLOOR
F(X)=(6-X)(4-X)
SYMBOLIC
OPERATIONS ON MULTIPLICATION, COEFFICIENTS, MULTIPLY VARIABLES
7X(X-3)=7X^2-21X
(2X-1)(X+2)=2X^2+4X-X-2=2X^2+3X-2
OPERATIONS ON MULTIPLICATION, COEFFICIENTS-dIVISION: FACTOR AND REDUCE-EXAMPLES
12X-6/6+ 6(X-2)=(X-2)
X^2+7X+6/(X+6)(X+1)/X+1=(X+6)[
OPERATIONS ON MULTIPLICATION, COEFFICIENTS, MULTIPLY VARIABLES-INEQUALITIES
SINGLE INEQUALITIES: ONLY ONE INEQUALITY SIGN DIVIDED/MULTIPLIED BY A NEGATIVE NUMBER THE INEQUALITY IS REVERSED
EXAMPLES OF INEQUALITES
5X+8<(LESS THEN OR EQUAL TWO) 8X =14
-3X+8<(LESSTHAN OR EQUAL TO-3X < ( LESS THAN OR EQUAL TO
X>(GTOET) -2 **DIRECTION OF INEQUALITY REVERSES DUE TO DIVISION BY A NEGATIVE
INQUALITIES_EXAMPLE 1
IN 2004 AAA ESTIMATED THAT THE COSE OF OPERATING A NEW FORD TAURUS WAS .71 CENTS A MILE.
tHIS DID NOT INCLUDE TEH CAR PAYMENT.
SELECT THE INEQUALITY THAT REPRESENTS TOTAL CAR EXPENSES OF $700 TO 1000.00 PER MONTH,
INCLUDING A CAR PAYMETN, IF M TO REPRESENTS THE AVERAGE NUMBER OF MILES TRAVLED IN A MONTH AND P REPRESENTS THE AVERAGE NUMBER OF MILES TRAVELED IN A MONTH AND P REPRESENTS THE MONTHLY CAR PAYMENT

B. 700<(LTOE).71M+P< (LTOE) 1000 REMEMEBER THAT YOUR MONEY EXPRESSIONS MUST BE THE SAME DENOMINATIONS
-CHANGE THE 71 CENTS TO .71 SO IT IS EXPRESSED IN DOLLRS
-THE CAR PAYMENT REMAINS THE SAME CONSTANT EACH MONTH AND THE UPSKEEP COST CHANGE DEPENDS ON MILAGE DRIVE
using the SEQUENCE BELOW, CONTINE TO GENERATE A DESCRIPTION OF THE PROCESS FO RDETERMING THE SUM OF THE INTERIOR ANGLES OF A POLYGON IN TERMS OF THE NUMBBER OF SIDES OF A POLYGON:
THE SHAPES WRITTEN OUT AND NOT SHOWN: A REGULAR TRIANGLE, A SQUARE WITH THE LINE ON THE SIDE, A POLYGON WITH A SMALLER BROKEN LINE TRIANGLE ON THE INSIDE, THEN TWO MORE POLYGONS TO THE RIGHT
**PROBLEM OF UNDERSTANDING
RDETERMING THE SUM OF THE INTERIOR ANGLES OF A POLYGON IN TERMS OF THE NUMBBER OF SIDES OF A POLYGON:
C) THE SUM OF THE INTERIOR ANGLES OF A POLYGON IS EQUAL TO =180 DEG. * THE NUMBER OF SIDES MINUS TWO)

THIS IS A PATTERN WITH A PATTERN PROBLEM. DRAW IN TEH DIAGONALS FOR THE LAST 2 POLYGONS. lOOK AT THE NUMBER OF TRIANGLES IN EACH POLYGON AND DETERMINE HOW THIS IS RELATED TO THE NUMBER OF SIDES. RECALL THAT TEH SUM OF THE ANGLES OF A TRIANGLE IS 180 DEG. ***RECALL THAT THE SUM OF THE ANGLES OF A TRIANGLE IS 180 DEG. SO THE SUM OF THE ANGLES OF NAY POLYGON IS THE NUMBER OF TRIANGLES FORMED BY A DIAGOANLF FROM ONE VERTEX TIMES 180 DEGREES. uSING THE NUMBER OF SIDES OF THE POLYGON THIS WOULD BE A THE THE (NUMBER OF SIDES - 2 *180 DEGREES)
IF YOU ARE COMF. YOU MAY WANT TO PUT IN FORMULA FORM